Name_________________________________________
Topic 2 Math and Measurement
Chapter ¾
1 Scientific method: Make observations and look for patterns.
vs. Theory –
Law -
Example: when wood burns it gets __________. When steel wool is heated it gets ___________.
How does atomic theory account for these changes?
LaVoisier
Experiment –
Results –
Law of conservation of mass
Particle diagram: Water reacts according to this equation: 2H2 + O2  2 H2O
Draw the products consistent with the law of conservation of mass
Question: If 4 grams of hydrogen combines with 32 grams of oxygen
What mass of water is formed?
Observations and measurements
Qualitative observations –
Ex:
vs.
Quantitative observations Ex:
Regents questions
1
2 - Scientific Notation consists of two parts:
Example:
Changing between forms:
289,800,000
0.000567
5.093 x 106
1.976 x 10-4
Learning check
1) 4057
2) 0.00387
3) 30000
4) 2
5) 0.4760
Calculating with Scientific notation
(3.0)(6.0 x 10 3)
(3.0)(6.0 x 10 -3)
(3.0 x 10 3)(6.0 x 10 3)
(3.0 x 10 2)(6.0 x 10 -5)
(6.0 x 103)
(3.0)
(6.0 x 103)
(3.0 x 102)
Learning check
1. (2.0)(6.3 x 10 4)
3. (2.0 x 10 -2)(6.3 x 10 4)
(3.0)
(6.0 x 10 3)
(3.0 x 10 2)
(6.0 x 10 3)
2. (6.4 x 10 4)
(2.0)
4. (6.4 x 10 4)
(2.0 x 10 -2)
Regent’s questions
2
3 - Accuracy and Precision
Accuracy -
Precision -
Percent error
Formula:
A student calculates the density of mercury to be 13.2 g/cm3. If the accepted value is 13.6 g/cm3, what is
the percentage error?
Negative error means? Try one:
At a track meet, your time a friend running 100 m in 11.00 seconds. The officials time her at 10.67
seconds. What is your percentage error?
Regents questions:
4 - Significant figures and precision
Significant figures (significant digits) include….
Reading a scale
l2. . . . I . . . . I3 . . . .I . . . . I4. .
Zero as a measured value
.l ....I....I ....I....I ..
3
4
cm
5
cm
3
Zeros as placeholders
Ex1:
Ex2:
Left after rounding: Ex:
Counting Significant figures
RULE All non-zero digits in a measured number are significant. Only a zeros can be used as placeholders.
Ex:
38.15 cm =
5.6 ft =
65.6 lb =
122.55 m =
RULE Zeros between nonzero numbers are significant. (They can not be rounded or dropped, unless they
are on an end of a number.)
Ex: 50.8 mm
2001 min
0.702 lb
0.00405 m
RULE Leading zeros in decimal numbers are NOT significant (they’re placeholders).
Ex: 0.008 mm
0.0156 oz
0.0042 lb
0.000262 mL
RULE . Trailing zeros in numbers without decimals are NOT significant. They are only serving as place
holders (left after rounding).
Ex; 25,000 in.
200. yr
48,600 gal
25,005,000 g
RULE . Trailing zeros in numbers with decimals are significant. They represent greater precision
Ex: 25.10 in.
20.0 yr
48.600 gal
25.0350 g
Pacific and Atlantic zeros:
LC:
A. Which answers contain 3 significant figures?
B. All the zeros are significant in
C. 534,675 rounded to 3 significant figures is
1) 0.4760
1) 0.00307
1) 535
2) 0.00476 3) 4760
2) 25.300 3) 2.050 x 103
2) 535,000 3) 5.35
LC
In which set(s) do both numbers contain the same number of significant figures?
1) 22.0 and 22.00 2) 400.0 and 40 3) 0.000015 and 150,000
Purpose of significant digits?
Adding and Subtracting with Significant digits
The answer has the same number of “tens places” as the measurement with the fewest tens places.
25.2
one decimal place
+ 1.35 two decimal places
LC: In each calculation, round the answer to the correct number of significant figures.
A. 235.05 + 19.6 + 2.1 =
1) 256.75
2) 256.8
3) 257
B.
58.925 - 18.2
=
1) 40.725
2) 40.73
3) 40.7
4
Multiplying and Dividing
Round (or add zeros to) the calculated answer until you have the same number of significant figures as the
measurement with the fewest significant figures.
Ex: 2.54 x 2.3 = 5.842 rounds to 5.8 (3 sig figures x 2 sig figures = round to 2 sig figures)
Learning Check
A. 2.19 X 4.2 =
1) 9
2) 9.2
3) 9.198
B.
C.
4.311 ÷ 0.07 =
2.54 X 0.0028
0.0105 X 0.060
1) 61.58
=
2) 62
1) 11.3
2) 11
3) 60
3) 0.041
Regents questions
5
5- Units and conversions Use SI units
Ex:
Metric Prefixes
Kilo- means 1000 of that unit ex: 1 kilometer (km) = 1000 meters (m)
1 kilo-unit = 1000 units
Ex: Air pressure is measured in pascals Normal air pressure is about
100 kilopascals. How many pascals is 100 kilopascal?
Centi- means 1/100 of that unit
ex: 1 meter (m) = 100 centimeters (cm)
1 unit = 100 centi-units
Milli- means 1/1000 of that unit
ex: 1 Liter (L) = 1000 milliliters (mL)
1 unit = 1000 milli-units
Atomic dimensions
A carbon atom has a radius of 91 picometers
Dimensional Analysis: Converting between units: Conversion Factors (fractions)
Fractions in which the numerator and denominator are EQUAL quantities expressed in different units
1 in. = 2.54 cm
Factors:
Learning Check
Write conversion factors that relate each of the following pairs of units:
1. Liters and mL
2. Hours and minutes
3. Meters and kilometers
Setting up conversions
How many minutes are in 2.5 hours?
Identify the starting and ending units:
Recognize the equality between the unit:
Build conversion factor with ending unit
starting unit
Setup to cancel units:
6
You have $7.25 in your pocket in quarters. How many quarters do you have?
How many quarters = 1 dollar?
How will we set up our conversion factor?
A practical problem: Driving in Canada, the speed limit says 90 km per hour, how fast is that in miles per
hour?
Step 1: ID Starting and ending unit
Step 2: Do I know an equality?
Step 3: Write down starting value and unit
Step 4: Write X conversion fraction
Step 5: cancel units and calculate
Calculating Fractions Review
3 x 4 =
2
3
4 x
4
2
=
8
x 1 =
2
Setup and convert the following using dimensional analysis
1) 26 miles to kilometers
2) 35.7 milliliters to liters
3) 10 grams of gold to cubic centimeters
(gold’s density is 19.32 g/cm3 )
6 - DENSITY - intensive physical property
Problems:
A piece of copper has a mass of 57.54 g.
It displaces 6.4 cm3. Calculate its density (g/cm3).
Mercury (Hg) has a density of 13.6 g/cm3.
What is the volume of 130 g of Hg in grams?
LC: Osmium has a density of 22.5 g/cm3.
What is the volume of a 50.00 g sample?
LC: What is the density (g/cm3) of 48 g of a metal if the metal
raises the level of water in a graduated cylinder from 25 mL to 33 mL?
7
Temperature Scales
Draw scales:
Notice…
But …
Celsius
vs.
Kelvin
Calculations Using Temperature:
K = ˚C + 273
or
˚C = K - 273
LC Room temperature is 298 Kelvins. What is this expressed in Celsius?
Regents Questions
8